as we move towards the right,the value of the numbers on a number line increases. The numbers to the left of zero are negative while the numbers to the right of zero are positive.
Therefore, by ordering the numbers from least to greatest, it would be
- 7, - 1, 1, 7
Identify the percent, amount, and base in this problem.
What percent of 80 is 40?
Step-by-step explanation:
well its going to be like this
80%/100 and 40/x
now to find the x you have to do cross products.
so 80% times 40
3200
the divide it by 100.
32
there you go
32 percent of 80 is 40
My question is #9 but I am confused if it is true or false
Given data:
The first condition is AB=XY.
The second condition is BC=YZ.
The third condition is ∠B=∠Y.
Follow the above condition then, triangle ABC is congruent to the triangle XYZ by SAS.
Thus, the first statement is true.
A store sells a $400 microscope after a markup of 32%. What is the price of the microscope at the store?
O $128
O $272
O $528
O $672
Using the markup, the price of the microscope at the store is 528 dollars.
What is markup?Markup shows how much more a company's selling price is than the amount the item costs the company.
In other words, markup is the amount by which the cost of a product is increased in order to derive the selling price.
Therefore, the store sells A store sells a $400 microscope after a markup of 32%. The price of the microscope at the store can be calculated as follows:
markup = 32% of 400
markup = 32 / 100 × 400
markup = 12800 / 100
markup = $128
Therefore,
price of the microscope = 400 + 128
price of the microscope = $528
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2x+3y=5 at (-2,3) find the equation of the tangent line
The slope of the tangent line to the line 2x+3y=5 can be found by differentiating 2x+3y=5.
Differentiating 2x+3y=5 with respect to x, we get
[tex]\begin{gathered} 2+3\frac{dy}{dx}=0 \\ 3\frac{dy}{dx}=-2 \\ \frac{dy}{dx}=\frac{-2}{3} \end{gathered}[/tex]m=dy/dx is the slope of tangent line.
Hence, slope, m=-2/3.
Now, the equation of the tangent line passing through point (x1, y1)=(-2, 3) with slope m=-2/3 can be found as,
[tex]\begin{gathered} m=\frac{y_1-y}{x_1-x} \\ \frac{-2}{3}=\frac{3-y}{-2-x} \\ -2(-2-x)=3(3-y) \\ 4+2x=9-3y \\ 3y+2x=5 \end{gathered}[/tex]Therefore, the equation of the tangent line is 3y+2x=5.
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Carter and Anna are making presentations for a class project. Carter's slideshow starts with a verbal introduction that is 13 seconds long, and then each slide is left up for 10 seconds. Anna leaves each slide onscreen for 6 seconds, and her introduction lasts 17 seconds. Carter and Anna notice that their presentations have both the same number of slides and the same duration. How long is each presentation? How many slides are in each presentation?
Given
Carter and Anna are making presentations for a class project.
Carter's slideshow starts with a verbal introduction that is 13 seconds long, and then each slide is left up for 10 seconds.
Anna leaves each slide onscreen for 6 seconds, and her introduction lasts 17 seconds.
Carter and Anna notice that their presentations have both the same number of slides and the same duration.
To find how long is each presentation and how many slides are in each presentation.
Now,
Let x be the time taken for each presentation and y be the number of slides.
Then, the equations are,
[tex]\begin{gathered} 13+10y=x\text{ \_\_\_\_(1)} \\ 17+6y=x\text{ \_\_\_\_\_(2)} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} 13+10y=17+6y \\ 10y-6y=17-13 \\ 4y=4 \\ y=1 \end{gathered}[/tex]Substitute y=1 in (1).
Then,
[tex]\begin{gathered} 13+10y=x \\ 13+10\times1=x \\ x=13+10 \\ x=23 \end{gathered}[/tex]Hence, the time taken for each presentation is 23 seconds and the number of slides is 1.
18 ÷ (-9)F. 9G. 2H. -2I. -9
We solve as follows:
[tex]\frac{18}{-9}=-2[/tex]So, the solution is h. -2
Graph: x < -2 I need help graphing this problem
Kindly check below.
1) Usually, whenever we need to graph an inequality, we need to treat it as if it was an equation.
2) So if we consider that x=-2 is a vertical line that passes through point -2, we can start with that.
3) Since the sign is < then we need to plot a dashed line delimiting the region to be shaded, given that -2 is not included. And finally, as it is lesser than -2 we can paint the region to the left of -2, where the numbers lesser than -2 are located.
4) So, our graph is:
5. The table shows the amount of money, A, in a savings account after mmonths. Select ALL the equations that represent the relationship betweenthe amount of money, A, and the number of months, m.*number ofmonthsdollaramount51,20061,30071,40081,500
Pick a situation related to your major that would be modeled by one of the models discussed in class. Describe why this model would be helpful. Models are any application/word problem used for exponential/logarithmic functions. For example, exponential growth or decay are models of exponential functions. Now, choose one that would fit with your career path and describe why it would be helpful.
To measure sound, we use the measure decibel which in fact is a logartimic funcion of the amplitude of a soud
To measure eartquakes, we use the Richter scale whci is a logaritmic function of the amplitude of the force of an earthquake
To calculate how long a body has been dead, the coroner must know how long the body temperature has not been at 98.6 degrees. Because the rate of the body cooling is proportionate to temperature differences between the body and its surroundings, the answer is found by calculating exponential decay using logarithms.
A zebra and a giraffe are having a race, 300 yards from a row of trees (the starting line) to the edge of a stream (the finish line). When they start evenly, the zebra wins the race by 50 yards.They decide to race again, but in the second race the zebra has to start 50 yards behind the row of trees (350 yards from the finish line), while the giraffe starts at the usual starting line. The zebra and the giraffe always run at the same speeds from race to race. Who wins the second race? Explain your reasoning.
A zebra and a giraffe are having a race, 300 yards from a row of trees (the starting line) to the edge of a stream (the finish line). When they start evenly, the zebra wins the race by 50 yards.
They decide to race again, but in the second race the zebra has to start 50 yards behind the row of trees (350 yards from the finish line), while the giraffe starts at the usual starting line. The zebra and the giraffe always run at the same speeds from race to race. Who wins the second race? Explain your reasoning.
we have that
The speed is equal to divide tthe distance by the time
speed=d/t
t=d/speed
The zebra and the giraffe always run at the same speeds from race to race.
so
Race 1
Zebra ------> t=300/speed1
giraffe ----> t=(300-50)/speed2 -----> t=250/speed2
where t is the finishing time of the zebra
equate both equations
300/speed1=250/speed2
300/250=speed1/speed2
1.2=speed1/speed2
speed1=1.2speed2
that means ----> the spped of the zebra is 1.2 times the speed of the giraffe
Race 2
Zebra ----> t1=350/(1.2speed2) ------> t1=292/speed2
Giraffe ----> t2=300/speed2 ------> t2=300/speed2
compare the times
t1 < t2
that means
the zebra wins the race 2You have 2 different savings accounts. For Account A, the simple interest earned after months is $. For Account B, the simple interest earned after months is $. If the interest rate is % for Account A and % for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer.
Question content area bottom
Part 1
Account A has a principal of $
enter your response here. (Round to the nearest dollar as needed.)
The principals of each account are given as follows:
Account A: $250.Account B: $400.The account that earned the most interest in the first month was Account A.
How to obtain the balance using simple interest?The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation presented as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.r is the interest rate, as a decimal.The interest accrued after t years is given as follows:
I(t) = Prt.
For Account A, the simple interest earned after 9 months is $6.94, considering a rate of 3.7%, hence the principal is obtained as follows:
6.94 = P x 0.037 x 9/12 (as the time is given in years)
0.02775P = 6.94
P = 6.94/0.02775
P = $250.
Then the interest during the first month was of:
I(1/12) = 250 x 0.037 x 1/12 = $0.77.
For the second account, considering the parameters, the principal is obtained as follows:
13.80 = P x 0.023 x 18/12
0.0345P = 13.80
P = 13.80/0.0345
P = $400.
Then the interest during the first month was of:
I(1/12) = 400 x 0.023 x 1/12 = $0.767. (which is less than account A).
Missing InformationThe problem is:
"You have 2 different savings accounts. For Account A, the simple interest earned after 9 months is $6.94. For Account B, the simple interest earned after 18 months is $13.80. If the interest rate is 3.7% for Account A and 2.3% for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer."
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c12334un567co89f(x)52241788794g(x)657929 l'12.3Use the table to evaluate the expression,(gºf)(3) =help (numbers)
Question:
Solution:
By definition of composition of functions, we have that:
[tex](g\circ f)(x)=\text{ g(f(x))}[/tex]Now, according to the table, if we evaluate above in x=3, we get:
[tex](g\circ f)(3)=\text{ g(f(3)) = g(2)=5}[/tex]so that, we can conclude that the correct answer is:
[tex](g\circ f)(3)=\text{5}[/tex]Find the product of the complex numbers. Leave your answer in polar form
Given: Two complex numbers below
[tex]\begin{gathered} z_1=2+2i \\ z_2=-3+3i \end{gathered}[/tex]To Determine: The product of the given complex numbers
[tex]z_1z_2=(2+2i)(-3+3i)[/tex][tex]\begin{gathered} z_1z_2=2(-3+3i)+2i(-3+3i) \\ z_1z_2=-6+6i-6i+6i^2 \\ z_1z_2=-6+6i^2 \end{gathered}[/tex]Please note that
[tex]\begin{gathered} i=\sqrt[]{-1} \\ i^2=(\sqrt[]{-1})^2_{} \\ i^2=-1 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} z_1z_2=-6+6i \\ z_1z_2=-6+6(-1) \\ z_1z_2=-6-6 \\ z_1z_2=-12+0i \end{gathered}[/tex]Let us convert the product to polar form
Please note that
[tex]\begin{gathered} if,z=x+iy,the\text{ polar form is} \\ z=r(\cos \theta+i\sin \theta) \\ \text{where} \\ r=\sqrt[]{x^2+y^2} \\ \tan \theta=\frac{y}{x} \\ \theta=tan^{-1}(\frac{y}{x}) \end{gathered}[/tex]Apply the conversion into the product we got
[tex]\begin{gathered} z_1z_2=-12+0i,x=-12,y=0 \\ r=\sqrt[]{x^2+y^2}=\sqrt[]{(-12)^2+0^2} \\ r=\sqrt[]{144+0} \\ r=\sqrt[]{144} \\ r=12 \\ \theta=\tan ^{-1}(\frac{0}{-12}) \\ \theta=\tan ^{-1}(0) \\ \theta=\pi \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} z_1z_2=r(\cos \theta+i\sin \theta) \\ r=12,\theta=\pi \\ z_1z_2=12(\cos \pi+i\sin \pi) \end{gathered}[/tex]Hence, the product of the complex numbers in polar form is
12(cosπ+isinπ)
You bought a notebook and four erasers at Target. The notebook cost 5$.You spent a total of 25$ at target. How much did each eraser cost
You bought:
1 notebook
4 eraser
Total Cost = 25.
Now, given Notebook = $5, so
25 - 5 = 20 dollars are left for [4 erasers]
So, each eraser would cost:
20/4 = 6 dollars
Thus,
Each Eraser Cost = $6
Which number is the solution of n/3 = - 12
-36 is the solution to the given equation
Here, we want to find the value of n that solves the equation
We simply cross-multiply here
We have;
[tex]n\text{ = 3 }\times\text{ -12 = -36}[/tex]Answer:
Step-by-step explanation:
1. The answer is -36 because -36/3=12.
Which two parallelograms have the same area? Figure 1 Figure 2 18 cm 4 cm 13 cm 1 1 15 Figure 4 cm Figure 3 11 cm 5 cm 6 cm 1 112
Figure 1 Area = 4 x 15 = 60 cm²
Figure 2 Area = 3 x 18 = 54 cm²
Figure 3 Area = 6 x 11 = 66 cm²
Figure 4 Area = 12 x 5 = 60 cm²
Answer:
Therefore area of figure 1 and 4 are equal
Tano went to a professional basketball game He spent $54.85 for a ticket S4 99 for a hot dog and $2 15 for a soda What is the total amount that he spent? Use mental math to find the sum. A S60.99 O B 961.00 O C 561.99 OD 96200
The total amount is calculated as the sum of the cost of the ticket, the cost of the hot dog, and the cost of the soda.
So, the total amount is:
[tex]54.85+4.99+2.15=61.99[/tex]Answer: $ 61.99
To answer it using mental math, we can add 0.85 and 0.15 and get 1, add 54 and 2 and get 56 and approximate 4.99 to 5.
Then, the sum 1 + 56 + 5 is equal to 62.00 but we need to subtract 0.01 because of the approximation. Therefore the final result is:
62.00 - 0.01 = 61.99
Give the domain of y = ln x.
Remember that
[tex]y=\ln x=\log _ex\Leftrightarrow e^y=x[/tex]And e^y can have any value in the interval (0, infinite).
Therefore, the domain of ln(x) is
[tex]\text{domain(}\ln (x))=(0,\infty)[/tex]The answer is x in (0, infinite)
The graph shown below displays thechange in the number of hurricanes thatoccurred over time.Which statement is the best description ofthe association between these variables?Choose 1 answer:A) As time went by, the number of hurricanestended to increase.B) As time went by, the number of hurricanestended to decrease.C) There is no clear relationship between timeand the number of hurricanes thatoccurred.
From the graph, it can be observed that number of hurricanes decreases as well as increases with increase in time (year since 1970). All points are distributed over the graph. So specific relation between number of hurricanes and time (year since 1970) can not be determined.
Thus option C is correct.
Las 25 22. Lines a and bare parallel and cut by the transversalt. Label each of the 7 unknown angles with the correct angle measure. 20 t
Explanation:
Angle b and the one that's 70º are vertical angles, so they are congruent.
Angles b and g are corresponding angles. They are congruent.
Angles g and e are vertical angles. They are congruent.
Angles a and b are supplementary - their measures add up 180º:
[tex]\begin{gathered} m\angle a+m\angle b=180º \\ m\angle a=180º-70º \\ m\angle a=110º \end{gathered}[/tex]Angles a and d are corresponding angles. They are congruent.
Angles c and a are vertical angles. They are congruent.
Angles d and f are vertical angles. They are congruent.
Answers:
• m∠a = 110º
,• m∠b = 70º
,• m∠c = 110º
,• m∠d = 110º
,• m∠e = 70º
,• m∠f = 110º
,• m∠g = 70º
write each degree measure in radians round to the nearest hundred 76 degrees 124 degrees and 149 degrees
Conversion from Degrees to Radians
One radian is equivalent to 180°
To convert from degrees to radians, we just multiply by the factor:
[tex]\frac{\pi}{180}[/tex]a) Convert 76 degrees to radians
[tex]76\cdot\frac{\pi}{180}=1.33\text{ rad}[/tex]b) Convert 124 degrees to radians
[tex]124\cdot\frac{\pi}{180}=2.16\text{ rad}[/tex]c) Convert 149 degrees to radians
[tex]149\cdot\frac{\pi}{180}=2.60\text{ rad}[/tex]use synthetic division to find the awnser write the quotient and write any remainders in fraction form (3x^3-x^2-9x+5)÷(x-2)
The given expressions are
[tex]\begin{gathered} 3x^3-x^2-9x+5 \\ x-2 \end{gathered}[/tex]We have to use the coefficients only to divide. Remember that the number 2 must multiply all the numbers in the quotient. The synthetic division would be:
x3 x2 x
| 3 -1 -9 5
2 | 6 10 2
3 5 1 7
Notice that the remainder is 7, the quotient would be the coefficients under the line.
The quotient is[tex]3x^2+5x^{}+1[/tex]Notice that the quotient doesn't include the number 7 because that's the remainder.
The remainder is 7.We can express the quotient, the remainder, and the divisor as follows:[tex]\frac{3x^3-x^2-9x+5}{x-2}=3x^2+5x+1+\frac{7}{x-2}[/tex]The mid point between T(-2,6) and J (-5,1)
To find the midpoint between two points wee need to apply the following formula:
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2} \\ y_m\text{ = }\frac{y_1+y_2}{2} \end{gathered}[/tex]Where (x1,y1) are the coordinates of the first point, (x2,y2) are the coordinates of the second point and (xm,ym) are the coordinates of the mid point. In this case the first point is T and the second point is J. If we apply the formula we should find the coordinates of the midpoint between them.
[tex]\begin{gathered} x_m\text{ = }\frac{-2-5}{2} \\ x_m\text{ = }\frac{-7}{2} \\ x_m\text{ = -3.5} \end{gathered}[/tex][tex]\begin{gathered} y_m\text{ = }\frac{6+1}{2} \\ y_m=\frac{7}{2} \\ y_m\text{ = 3.5} \end{gathered}[/tex]The coordinates of the midpoint are (-3.5, 3.5).
The ratio of men to women in a certain factory is 3 to 4. There are 228 men. find the number of women
Given
The ratio of men to women in a certain factory is 3 to 4. There are 228 men. find the number of women
Solution
Let the number of women be x
[tex]\begin{gathered} Men\text{ : Women} \\ 3\text{ : 4} \\ 228:\text{ x} \end{gathered}[/tex][tex]\frac{3}{4}=\frac{228}{x}[/tex]cross multiply
[tex]\begin{gathered} 3\times x=4\times228 \\ 3x=912 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{3x}{3}=\frac{912}{3} \\ \\ x=304 \end{gathered}[/tex]The number of women is 304
which of the following sets of numbers could represent the three sides of a triangle. 4,7,1212,16,284,12,137,13,22
ANSWER
4, 12, 13
EXPLANATION
The sum of any 2 sides of a triangle must be greater than the measure of the third side.
For these options we have to check which set of numbers follow this rule:
[tex]\begin{gathered} 4+7>12 \\ 11>12\text{ }\rightarrow\text{ false} \end{gathered}[/tex][tex]\begin{gathered} 12+16>28 \\ 28>28\text{ }\rightarrow\text{ false} \end{gathered}[/tex][tex]\begin{gathered} 4+12>13 \\ 16>13\text{ }\rightarrow\text{ true} \\ 12+13>4 \\ 25>4\text{ }\rightarrow\text{ true} \\ 4+13>12 \\ 17>12\text{ }\rightarrow\text{ true} \end{gathered}[/tex][tex]\begin{gathered} 7+13>22 \\ 20>22\rightarrow\text{ false} \end{gathered}[/tex]The third set of numbers could represent the three sides of a triangle
Determine the number of significant figures in the measurement 77.09 m.Express your answer numerically as an integer.
Given:
The significant figures in 77.09 m are 4 because all the digits are necessary to denote the quantity.
Hence, 4 is the number of significant figures expressed in integer.
Z1 and Z2 are a linear pair and the mZ1 is 9 times the measure of Z2. Find mZ1.mZ1 =degrees
The winter clothing drive has received donations of 15 coats, 27 pairs of gloves, 38 scarves, and 20 hats so far. Based on this data, what is a reasonable estimate of the probability that the next donation is not a pair of gloves? A: .54 B: .73C: .27 D: .37
we must add all the garments that are not gloves and divide them by the total
we add 15 coats, 38 scarves and 20 hats
[tex]15+38+20=73[/tex]and divide by the total
[tex]15+38+20+27=100[/tex][tex]\frac{73}{100}=0.73[/tex]so, the right option is B
The coordinates of the terminal point of the vector <9,4> with its initialpoint is at (-3, 2) is (a, b). State the value of a + 2b. *
Answer:
[tex]a+2b=18[/tex]Step-by-step explanation:
The vector in component form is given as:
[tex][/tex]Therefore, if the vector <9,4> has initial point at (-3, 2), to find the terminal point:
[tex]\begin{gathered} 9=x_2-(-3) \\ 4=y_2-2 \end{gathered}[/tex]Solve for x2 and y2.
[tex]\begin{gathered} x_2=9-3=6 \\ y_2=4+2=6 \end{gathered}[/tex]Terminal point (a,b) would be (6,6), hence the value of a+2b:
[tex]\begin{gathered} a+2b=6+2(6) \\ a+2b=18 \end{gathered}[/tex]To estimate the height of a building, two students find the angle of elevation from a point (at ground levedown the street from the building to the top of the building is 30°. From a point that is 400 feet closer tothe building, the angle of elevation (at ground level) to the top of the building is 52°. If we assume thatthe street is level, use this information to estimate the height of the building.The height of the building isfeet.
Given:
ground to building top is 30 degrees.
Distance = 400 feet
The angle of elevation at is top of the building = 52 degrees.
Find-: Height of the building.
Sol:
For the triangle ABC
Perpendicular = Height
Base = x
Angle = 52
Use trigonometric formula:
[tex]\begin{gathered} \tan\theta=\frac{\text{ Perpendicular}}{\text{ Base}} \\ \\ \tan52=\frac{H}{x} \\ \\ 1.2799=\frac{H}{x} \\ \\ x=\frac{H}{1.2799} \end{gathered}[/tex]For the triangle ABD is:
Perpendicular = Height
Base = x+400
Angle = 32
[tex]\begin{gathered} \tan\theta=\frac{\text{ Perpendicular}}{\text{ Base}} \\ \\ \tan32=\frac{H}{x+400} \\ \\ 0.6249=\frac{H}{x+400} \\ \\ \end{gathered}[/tex]Put the value of "x" is:
[tex]\begin{gathered} 0.6249(x+400)=H \\ \\ 0.6249x+249.947=H \\ \\ 0.6249(\frac{H}{1.2799})+249.947=H \\ \\ 0.488H+249.947=H \\ \\ 0.512H=249.947 \\ \\ H=488.407 \\ \end{gathered}[/tex]So the height of the building is: 488.407 feet